Deformation Theory of Algebras and Their Diagrams

Author: Martin Markl

Publisher: American Mathematical Soc.

ISBN: 0821889796

Category: Mathematics

Page: 129

View: 4038

This book brings together both the classical and current aspects of deformation theory. The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. In the interest of readability, some technically complicated proofs have been omitted when a suitable reference was available. The relation between the uniform continuity of algebraic maps and topologized tensor products is explained in detail, however, as this subject does not seem to be commonly known and the literature is scarce. The exposition begins by recalling Gerstenhaber's classical theory for associative algebras. The focus then shifts to a homotopy-invariant setup of Maurer-Cartan moduli spaces. As an application, Kontsevich's approach to deformation quantization of Poisson manifolds is reviewed. Then, after a brief introduction to operads, a strongly homotopy Lie algebra governing deformations of (diagrams of) algebras of a given type is described, followed by examples and generalizations.

Deformation Theory

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN: 1441915958

Category: Mathematics

Page: 234

View: 9250

The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.

Arithmetic and Geometry Around Galois Theory

Author: Pierre Dèbes,Michel Emsalem,Matthieu Romagny,A. Muhammed Uludağ

Publisher: Springer Science & Business Media

ISBN: 3034804873

Category: Mathematics

Page: 404

View: 5044

This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.​

Automorphe Formen

Author: Anton Deitmar

Publisher: Springer-Verlag

ISBN: 3642123902

Category: Mathematics

Page: 252

View: 9166

Das Buch bietet eine Einführung in die Theorie der automorphen Formen. Beginnend bei klassischen Modulformen führt der Autor seine Leser hin zur modernen, darstellungstheoretischen Beschreibung von automorphen Formen und ihren L-Funktionen. Das Hauptgewicht legt er auf den Übergang von der klassischen, elementaren Sichtweise zu der modernen, durch die Darstellungstheorie begründete Herangehensweise. Diese Art der Verbindung von klassischer und moderner Sichtweise war in der Lehrbuchliteratur bisher nicht zu finden.

Kombinatorische Optimierung

Theorie und Algorithmen

Author: Bernhard Korte,Jens Vygen

Publisher: Springer-Verlag

ISBN: 3540769196

Category: Mathematics

Page: 675

View: 704

Das Lehrbuch ist die deutsche Übersetzung der 4., wesentlich erweiterten Auflage des Titels „Combinatorial Optimization – Theory and Algorithms". Es gibt den neuesten Stand der kombinatorischen Optimierung wieder und liefert vornehmlich theoretische Resultate und Algorithmen mit beweisbar guten Laufzeiten und Ergebnissen, jedoch keine Heuristiken. Enthalten sind vollständige Beweise, auch für viele tiefe und neue Resultate, von denen einige bisher in der Lehrbuchliteratur noch nicht erschienen sind. Mit Übungen und umfassendem Literaturverzeichnis.

Introduction to Knot Theory

Author: R. H. Crowell,R. H. Fox

Publisher: Springer Science & Business Media

ISBN: 1461299357

Category: Mathematics

Page: 182

View: 3340

Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space. It is a meeting ground of such diverse branches of mathematics as group theory, matrix theory, number theory, algebraic geometry, and differential geometry, to name some of the more prominent ones. It had its origins in the mathematical theory of electricity and in primitive atomic physics, and there are hints today of new applications in certain branches of chemistryJ The outlines of the modern topological theory were worked out by Dehn, Alexander, Reidemeister, and Seifert almost thirty years ago. As a subfield of topology, knot theory forms the core of a wide range of problems dealing with the position of one manifold imbedded within another. This book, which is an elaboration of a series of lectures given by Fox at Haverford College while a Philips Visitor there in the spring of 1956, is an attempt to make the subject accessible to everyone. Primarily it is a text book for a course at the junior-senior level, but we believe that it can be used with profit also by graduate students. Because the algebra required is not the familiar commutative algebra, a disproportionate amount of the book is given over to necessary algebraic preliminaries.

Ebene algebraische Kurven

Author: Egbert Brieskorn,Horst Knörrer

Publisher: N.A


Category: Mathematics

Page: 964

View: 4692

Encyclopedia of mathematical physics

Author: Sheung Tsun Tsou

Publisher: Academic Pr

ISBN: 9780125126601

Category: Science

Page: 3500

View: 6824

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.

Deformation Theory of Plasticity

Author: Robert Millard Jones

Publisher: Bull Ridge Corporation

ISBN: 0978722310

Category: Deformations (Mechanics)

Page: 622

View: 5055

Minimal Resolutions Via Algebraic Discrete Morse Theory

Author: Michael Jöllenbeck,Volkmar Welker

Publisher: American Mathematical Soc.

ISBN: 0821842579

Category: Mathematics

Page: 74

View: 7180

Forman's discrete Morse theory is studied from an algebraic viewpoint. Analogous to independent work of Emil Skoldberg, the authors show that this theory can be aplied to chain complexes of free modules over a ring and provide four applications of this theory.

Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians

Author: Francis Nier,Bernard Helffer

Publisher: Springer Science & Business Media

ISBN: 9783540242000

Category: Mathematics

Page: 209

View: 4586

There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations, and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction, this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart, the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes, and the Morse inequalities.

Non-Linear Elastic Deformations

Author: R. W. Ogden

Publisher: Courier Corporation

ISBN: 0486318710

Category: Technology & Engineering

Page: 544

View: 1701

Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

Geometric Continuum Mechanics and Induced Beam Theories

Author: Simon R. Eugster

Publisher: Springer

ISBN: 3319164953

Category: Technology & Engineering

Page: 146

View: 666

This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.

Particles, Fields, and Gravitation

Lodz, Poland, 15-19 April 1998

Author: Jakub Rembielinski

Publisher: American Inst. of Physics


Category: Science

Page: 585

View: 5016

The 54 papers discuss many aspects of contemporary theoretical and mathematical physics, among them quantum deformations and noncommutative geometry, quantum mechanics, quantum and topological field theory, solvable and quasi-solvable models, modern gravitation theory, and geometrical methods in phy

Iwasawa Theory 2012

State of the Art and Recent Advances

Author: Thanasis Bouganis,Otmar Venjakob

Publisher: Springer

ISBN: 3642552455

Category: Mathematics

Page: 483

View: 9850

This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan).